1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
loris [4]
3 years ago
13

Let v = (v1, v2) be a vector in r2. show that (v2, −v1) is orthogonal to v, and use this fact to find two unit vectors orthogona

l to the given vector. v = (9, 40)
Mathematics
2 answers:
hodyreva [135]3 years ago
3 0
Because v1 x v2 + v2 x (-v1) = v1 x v2 - v2 x v1 = v1 x v2 - v1 x v2 = 0, vector (v1,v2) is orthogonal to (v2,-v1);
Let (a,b) be an unit vector orthogonal to (9,40);
So, a^2 + b^2 = 1 and a x 9 + b x 40 = 0;
Then, a = - 40 x b / 9;
Finally, 160 x b^2 / 81 + b^2 = 1;
160 x b^2 + 81 x b^2 = 81;
241 x b^2 = 81;
b^2 = 81 / 241;
b = + or - 9/\sqrt{241}
a = + or - 40/\sqrt{241}
We have (+40/\sqrt{241};9/\sqrt{241}) and (-40/\sqrt{241};-9/\sqrt{241});
Maslowich3 years ago
3 0

Answer:

\hat{u_1}=(\frac{40}{41},-\frac{9}{40}) and \hat{u_2}=(\frac{-40}{41},\frac{9}{41})

Step-by-step explanation:

We are given that v=(v_1,v_2) be a vector in R^2.

We have to show that (v_2,-v_1) is orthogonal to v.We have to find the two unit vector orthogonal to the given vector v=(9,40).

Orthogonal vectors:If two vectors u and v are orthogonal then

u\cdot v=u_1v_2+u_2v_1=0

Using this condition

(v_1,v_2)\cdot (v_2,-v_1)

=v_1v_2-v_2v_1=0

Hence, (v_2,-v_1) is orthogonal to v.

By using this fact then, we get

u_1=(40,-9) is orthogonal to v=(9,40)

Unit vector=\frac{\vec{a}}{\mid a\mid}

\mid u_1\mid=\sqrt{(40)^2+(-9)^2}=41

\hat{u_1}=(\frac{40}{41},-\frac{9}{40})

u_2=(-40,9) is orthogonal to v=(9,40)

\mid u_2\mid=\sqrt{(-40)^2+9^2}=41

\hat{u_2}=(\frac{-40}{41},\frac{9}{41})

The two unit vectors which are orthogonal to given vector v=(9,40) are given by

\hat{u_1}=(\frac{40}{41},-\frac{9}{40}) and \hat{u_2}=(\frac{-40}{41},\frac{9}{41})

You might be interested in
A retailer has determined that the cost C of
adelina 88 [10]
A. The expression given in the question is

c = 6x + (900000/x)
c = (6x^ +900000)/x
I hope that this is the expression that you were looking for.

b. When x = 240, then

c = [6 * (240)^2 + 900000]/ 240
   = (6 * 57600) + 900000/240
   = (345600 + 900000)/240
   = 5190

From the above deduction, it can be concluded that the cost of ordering and storing is 5190. I hope the procedure is clear enough for you to understand.
7 0
3 years ago
Select the number and name of the terms below (select 2): 2121
mihalych1998 [28]
Its a monomial and it has 4 terms
6 0
3 years ago
Bonita makes $11.75/hour and Bruce
lbvjy [14]
C is the answer you get while doing the math
4 0
3 years ago
HEY CAN ANYONE PLS ANSWER DIS MATH QUESTION RQ!!!
ikadub [295]

Answer:

(3,3) (2,2) (1,1) (0,0) (-1,-1)

Step-by-step explanation:

the equation for this table will b y=x which is a linear equation and graph

3 0
3 years ago
Your bill at dinner is $25. Sales tax is 8.1% and you will tip 18%. What is your total.
Over [174]

Answer:

31.525

Step-by-step explanation:

first you calculate the tip, 0.18*25 is 4.5

then you calculate the tax, 0.081*25 is 2.025

finally you add everything together, 25+4.5+2.025 is 31.525

8 0
2 years ago
Other questions:
  • Brainliest!
    13·2 answers
  • 1 ½ x 4 2/9 = <br><br> 2 ⅘ x ⅕ = <br><br> 4 3/7 x ⅚ =<br><br> 6/6 x 1 ¼ = 1 ¼
    10·1 answer
  • 3 pizzas for $ 16.50 what is the unit rate for one pizza
    14·2 answers
  • What is the answer to 3x+5y=1; -6x-10y=14
    12·1 answer
  • I need to know the answers because my friends and I cannot have different answer.
    11·1 answer
  • HELP URGENT!!!!!!!!!!!!!!!!!!!!!!!!!
    9·2 answers
  • Find the number that if subtracted from 7 and 12, the product of the two numbers gives 104
    13·1 answer
  • If 3.485÷5.1 is random long division form so that advisor is rain as a whole number where one the decimal point the place in the
    8·1 answer
  • 3.
    10·2 answers
  • What is the value of x?<br>log 3x =4<br> A. 7 B. 27 C. 81 D. 12
    15·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!